Some surprising results from the analytical design of high-NA aplanatic singlet lenses with only one aspheric surface

Abstract

Both spherical aberration and linear coma are corrected (i.e. the Abbe Sine Condition) in an aplanatic optical system which besides diffraction-limited axial imagery, tend to be less sensitive to misalignments. In general this can be accomplished by properly aspherizing two sufficiently separated surfaces such as in the Ritchey-Chretien telescope. However for a practical focusing or collimating singlet lens with object at infinity, there are relatively straightforward analytical solutions in which spherical is corrected by just one asphere and coma by either the thickness or shape (bending) factor. This is exactly true to third-order and nearly so to all orders even for numerical apertures (NA) approaching one. The solutions yield some surprising results not only for the common convex-plano case, but also highly meniscus lenses with large or even infinite shape factors.